/// <summary>
/// Performs the scalar multiplication of <paramref name="N"/>*<paramref name="P"/>.
/// </summary>
/// <param name="N">Scalar, in binary, little-endian form.</param>
/// <param name="P">Point</param>
/// <param name="Normalize">If normalized output is expected.</param>
/// <returns><paramref name="N"/>*<paramref name="P"/></returns>
public override PointOnCurve ScalarMultiplication(byte[] N, PointOnCurve P, bool Normalize)
{
PointOnCurve Result = base.ScalarMultiplication(N, P, Normalize);
if (Normalize)
{
Result.Normalize(this);
}
return(Result);
}
/// <summary>
/// Verifies a signature of <paramref name="Data"/> made by the EdDSA algorithm.
/// </summary>
/// <param name="Data">Payload to sign.</param>
/// <param name="PublicKey">Public Key of the entity that generated the signature.</param>
/// <param name="HashFunction">Hash function to use.</param>
/// <param name="Curve">Elliptic curve</param>
/// <param name="Signature">Signature</param>
/// <returns>If the signature is valid.</returns>
public static bool Verify(Stream Data, byte[] PublicKey, HashFunctionStream HashFunction,
EdwardsCurveBase Curve, byte[] Signature)
{
try
{
int ScalarBytes = Signature.Length;
if ((ScalarBytes & 1) != 0)
{
return(false);
}
ScalarBytes >>= 1;
byte[] R = new byte[ScalarBytes];
Array.Copy(Signature, 0, R, 0, ScalarBytes);
PointOnCurve r = Decode(R, Curve);
byte[] S = new byte[ScalarBytes];
Array.Copy(Signature, ScalarBytes, S, 0, ScalarBytes);
BigInteger s = EllipticCurve.ToInt(S);
byte[] h;
if (s >= Curve.Order)
{
return(false);
}
using (TemporaryStream TempFile = new TemporaryStream()) // dom2(F, C) = blank string
{
TempFile.Write(R, 0, ScalarBytes);
TempFile.Write(PublicKey, 0, ScalarBytes);
Data.Position = 0;
Data.CopyTo(TempFile); // PH(M)=M
TempFile.Position = 0;
h = HashFunction(TempFile);
}
BigInteger k = BigInteger.Remainder(EllipticCurve.ToInt(h), Curve.Order);
PointOnCurve P1 = Curve.ScalarMultiplication(s, Curve.BasePoint, false);
PointOnCurve P2 = Curve.ScalarMultiplication(k, Curve.Decode(PublicKey), false);
Curve.AddTo(ref P2, r);
P1.Normalize(Curve);
P2.Normalize(Curve);
return(P1.Equals(P2));
}
catch (ArgumentException)
{
return(false);
}
}
/// <summary>
/// Verifies a signature of <paramref name="Data"/> made by the ECDSA algorithm.
/// </summary>
/// <param name="Data">Payload to sign.</param>
/// <param name="PublicKey">Public Key of the entity that generated the signature.</param>
/// <param name="HashFunction">Hash function to use.</param>
/// <param name="Curve">Elliptic curve</param>
/// <param name="ScalarBytes">Number of bytes to use for scalars.</param>
/// <param name="MsbMask">Mask for most significant byte.</param>
/// <param name="Signature">Signature</param>
/// <returns>If the signature is valid.</returns>
public static bool Verify(byte[] Data, byte[] PublicKey, HashFunction HashFunction,
int ScalarBytes, byte MsbMask, PrimeFieldCurve Curve, byte[] Signature)
{
int c = Signature.Length;
if (c != ScalarBytes << 1)
{
return(false);
}
c >>= 1;
byte[] Bin = new byte[c];
Array.Copy(Signature, 0, Bin, 0, c);
BigInteger r = EllipticCurve.ToInt(Bin);
Bin = new byte[c];
Array.Copy(Signature, c, Bin, 0, c);
BigInteger s = EllipticCurve.ToInt(Bin);
PointOnCurve PublicKeyPoint = Curve.Decode(PublicKey);
if (!PublicKeyPoint.NonZero || r.IsZero || s.IsZero || r >= Curve.Order || s >= Curve.Order)
{
return(false);
}
BigInteger e = CalcE(Data, HashFunction, ScalarBytes, MsbMask);
BigInteger w = Curve.ModulusN.Invert(s);
BigInteger u1 = Curve.ModulusN.Multiply(e, w);
BigInteger u2 = Curve.ModulusN.Multiply(r, w);
PointOnCurve P2 = Curve.ScalarMultiplication(u1, Curve.BasePoint, true);
PointOnCurve P3 = Curve.ScalarMultiplication(u2, PublicKeyPoint, true);
Curve.AddTo(ref P2, P3);
if (!P2.NonZero)
{
return(false);
}
P2.Normalize(Curve);
BigInteger Compare = BigInteger.Remainder(P2.X, Curve.Order);
if (Compare.Sign < 0)
{
Compare += Curve.Order;
}
return(Compare == r);
}
/// <summary>
/// Verifies a signature of <paramref name="Data"/> made by the EdDSA algorithm.
/// </summary>
/// <param name="Data">Payload to sign.</param>
/// <param name="PublicKey">Public Key of the entity that generated the signature.</param>
/// <param name="HashFunction">Hash function to use.</param>
/// <param name="Curve">Elliptic curve</param>
/// <param name="Signature">Signature</param>
/// <returns>If the signature is valid.</returns>
public static bool Verify(byte[] Data, byte[] PublicKey, HashFunctionArray HashFunction,
EdwardsCurveBase Curve, byte[] Signature)
{
try
{
int ScalarBytes = Signature.Length;
if ((ScalarBytes & 1) != 0)
{
return(false);
}
ScalarBytes >>= 1;
byte[] R = new byte[ScalarBytes];
Array.Copy(Signature, 0, R, 0, ScalarBytes);
PointOnCurve r = Decode(R, Curve);
byte[] S = new byte[ScalarBytes];
Array.Copy(Signature, ScalarBytes, S, 0, ScalarBytes);
BigInteger s = EllipticCurve.ToInt(S);
if (s >= Curve.Order)
{
return(false);
}
int c = Data.Length;
byte[] Bin = new byte[(ScalarBytes << 1) + c]; // dom2(F, C) = blank string
Array.Copy(R, 0, Bin, 0, ScalarBytes);
Array.Copy(PublicKey, 0, Bin, ScalarBytes, ScalarBytes);
Array.Copy(Data, 0, Bin, ScalarBytes << 1, c); // PH(M)=M
byte[] h = HashFunction(Bin);
BigInteger k = BigInteger.Remainder(EllipticCurve.ToInt(h), Curve.Order);
PointOnCurve P1 = Curve.ScalarMultiplication(s, Curve.BasePoint, false);
PointOnCurve P2 = Curve.ScalarMultiplication(k, Curve.Decode(PublicKey), false);
Curve.AddTo(ref P2, r);
P1.Normalize(Curve);
P2.Normalize(Curve);
return(P1.Equals(P2));
}
catch (ArgumentException)
{
return(false);
}
}